Constitutive relations for the shear band evolution in granular matter under large strain

Luding, Stefan

doi:10.1016/j.partic.2008.07.020

Cited by 43 publications

(86 citation statements)

References 16 publications

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“…with the isotropic stress p and the deviatoric stress q = (σ max − σ min )/2, which is based on the maximal and minimal eigenvalues of stress [11,12] (which are usually not known when only one normal and one shear stress can be measured). Note that p is objective and well-defined (but not always available).…”

Section: Theoretical Interpretationmentioning

confidence: 99%

“…This is in contrast to σ * , which depends on the experimental configuration and the details of the measurement. In general, one has p = σ * and q = τ * even though the values are close [12]. An alternative definition of the deviatoric stress is based on the second invariant of the stress tensor and is thus objective: σ D = √ I 2 /2, see Ref.…”

Section: Theoretical Interpretationmentioning

confidence: 99%

“…An alternative definition of the deviatoric stress is based on the second invariant of the stress tensor and is thus objective: σ D = √ I 2 /2, see Ref. [12]. For a stress tensor with intermediate eigenvalue σ 2 = (σ max + σ min )/2, which is colinear (coaxial) with the strain-rate in the critical-state, the three deviatoric stresses would be identical τ * = q = σ D .…”

Section: Theoretical Interpretationmentioning

confidence: 99%

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The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

Luding¹,

Alonso‐Marroquín

2011

Granular Matter

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Dry granular materials in a split-bottom ring shear cell geometry show wide shear bands under slow, quasistatic, large deformation. This system is studied in the presence of contact adhesion, using the discrete element method (DEM). Several continuum fields like the density, the deformation gradient and the stress tensor are computed locally and are analyzed with the goal to formulate objective constitutive relations for the flow behavior of cohesive powders. From a single simulation only, by applying time-and (local) space-averaging, and focusing on the regions of the system that experienced considerable deformations, the critical-state yield stress (termination locus) can be obtained. It is close to linear, for non-cohesive granular materials, and nonlinear with peculiar pressure dependence, for adhesive powdersdue to the nonlinear dependence of the contact adhesion on the confining forces. The contact model is simplified and possibly will need refinements and additional effects in order to resemble realistic powders. However, the promising method of how to obtain a critical-state yield stress from a single numerical test of one material is generally applicable and waits for calibration and validation.

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Section: Theoretical Interpretationmentioning

confidence: 99%

Section: Theoretical Interpretationmentioning

confidence: 99%

Section: Theoretical Interpretationmentioning

confidence: 99%

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The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

Luding¹,

Alonso‐Marroquín

2011

Granular Matter

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“…The deviatoric stress, D , is calculated from the three normal stresses using equation 9 (Luding, 2008).…”

Section: Stress and Strain Rate Analysismentioning

confidence: 99%

Prediction of attrition in agitated particle beds

Hare

Ghadiri

Dennehy

2011

Chemical Engineering Science

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The majority of pharmaceutical powders produced through crystallisation are dried in agitated dryers. The rotation of the impeller causes shear deformation of the bed, which enhances the drying rate, but also leads to particle breakage. A method of predicting the extent of breakage occurring due to agitation is described and applied for Paracetamol in a small-scale dryer. The distributions of stresses and strains in the bed are estimated using the Distinct Element Method (DEM). The information obtained here is then coupled with the measured attrition of Paracetamol in an annular shear cell in order to predict the attrition in the agitated bed. The experiments are carried out on dry material so as to establish purely the effect of stresses and strains on attrition, whilst keeping moisture content and temperature constant.The shear cell provides uniform condition for stresses and strains so that the breakage taking place under relatively well-defined conditions is quantified. In contrast, the prevailing shear stresses and strains in the agitated bed have wide distributions, as little shearing takes place near the impeller shaft, whilst there are considerable shearing stresses near the impeller tip. Therefore the bed is divided into a number of segments for which the extent of attrition can be evaluated for each segment, based on the shear cell data. A good quantitative agreement is found between the predictions and experimental results obtained for the attrition of Paracetamol in the small scale dryer. The resulting prediction also suggests that, for a given number of impeller rotations, the extent of breakage is independent of impeller speed in the range tested (20 -78 rpm). This is expected as the prevailing strain rates are too low for the inertial effects to be dominating and the shear stresses are independent of shear rates within the range investigated. The attrition prediction suggest that over half of the attrition occurs in the bottom third of the bed, with increased attrition at greater radial distances. The attrition is also predicted to occur predominantly 30 o in front of and behind the impeller.

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“…Rheometry and modelling of powder behaviour under the dynamic flow conditions have received some attention in recent years (Freeman, 2007;Klein et al, 2003;Langroudi et al, 2010;Luding, 2008;Savage, 1998;Tardos, 1997;Tardos et al, 2003). Tardos et al (2003) analysed particle flows inside a Couette device consisting of two concentric cylinders with differential rotational speeds, thus forming a shear band.…”

Section: Introductionmentioning

confidence: 99%

Analysis of powder rheometry of FT4: Effect of air flow

Nan

Ghadiri

Wang

2017

Chemical Engineering Science

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Understanding of particle flow behaviour as a function of strain rate is of great interest in many items of equipment of industrial processes, such as screw conveyors, impeller mixers, and feeders, etc. The traditional commercial instruments for bulk powder flow characterisation, such as shear cells, operate at low shear strain rates, and are not representative of unit operations under dynamic conditions. In recent years, the FT4 powder rheometer of Freeman Technology has emerged as a widely used technique for characterising particle flow under dynamic conditions of shear strain rate; yet little is known about its underlying powder mechanics. We analyse the effect of gas flow on the flow behaviour of cohesionless particles in FT4 both experimentally and by numerical simulations using the combined discrete element method (DEM) and computational fluid dynamics (CFD). The results show that the effect of gas flow on the flow energy could be described by the resultant fluid-induced drag on the particles above the blade position as the impeller penetrates the bed. The strain rate in front of the blade is mainly determined by the impeller tip speed, and is not sensitive to the gas flow and particle size. The flow energy correlates well with the shear stress in front of the blade. They both increase with the strain rate and are significantly reduced by the upward gas flow.

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Constitutive relations for the shear band evolution in granular matter under large strain

Cited by 43 publications

References 16 publications

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

Prediction of attrition in agitated particle beds

Analysis of powder rheometry of FT4: Effect of air flow

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